Rodriguez came on for Cristiano Ronaldo in the second half at the Santiago Bernabeu and found the back of the net in the 80th minute after he pounced on a loose ball in the penalty area following an attempt by Benzema.
Raul Garcia equalized for Atletico in the 87th from a corner.
Throughout the first half, Atletico held Madrid in check by dominating the midfield with disciplined tackling and ensuring at least two players shadowed forwards Gareth Bale and Ronaldo every time a pass was made to them.
Rodriguez joined Xabi Alonso, Toni Kroos and Angel Di Maria in Madrid's midfield and was brought on by coach Carlo Ancelotti after Ronaldo had been seen holding and rubbing his left leg late in the first half. Di Maria had come on in the second half for Luka Modric.
''He did well,'' Ancelotti said of James. ''All the second half the team played with greater speed and intensity, looking for chances from the wings. He scored and that'll give him more confidence.''
The match was preceded by a tribute to Madrid great Alfredo Di Stefano, who died in July. A string quartet played as the club displayed large photographs of the forward and the silverware he helped win to the crowd.
Tennis player Rafael Nadal, who this week said he will not be defending his US Open title, watched the match from the VIP stand.
''Kroos is an important player and a great signing for Real Madrid,'' Nadal said at half time.
Madrid began with captain Iker Casillas in goal. He was tested twice in the first 15 minutes by shots from Saul Niguez and Mario Mandzukic.
Atletico played a physical game throughout and defender Guilhelmo Siqueira was the first to be shown a yellow card after fouling Bale on the right touchline in the 13th minute.